
Originally Posted by
AntonioLao
Using spreadsheet software an m by n infinite ordered matrix can be finitely modeled for finite arbitrary numbers of m-row and n-column such that m and n vary from 0, 1, 2, 3, 4, 5, 6, 7, 8…. For each matrix element calculation as a function of both m and n by this expression: e(m, n)=2m+3n. It can be noted that the following elements are prime numbers: (1,0)=2, (0,1)=3, (1,1)=5, (2,1)=7, (1,3)=11, (5,1)=13, (7,1)=17, (8, 1)=19, (10, 1)=23, (13, 1)=29, (14,1)=31, (17,1)=37, (19,1)=41, (20,1)=43, so on and so forth. Furthermore there are patterns of alternate even and odd columns with prime pattern distributions of single prime and twin primes. Likewise, the rows alternate between single row of mixed odd and even composite numbers and two consecutive rows of primes. Moreover, the entire set of whole numbers with the exception of unity are repeated in a pattern from lower left to upper right on both side of the diagonal. The elements along the diagonal are increasing multiples of 5. The numbers that are not repeated are: 0, 2, 3, 4, 5, 7. the numbers repeated twice are: 6, 8, 9, 10, 11, and 13. The numbers repeated 3 times are: 12, 14, 15, 16, 17, and 19. The numbers repeated 4 times are: 18, 20, 21, 22, 23, and 25. The numbers repeated 5 times are: 24, 26, 27, 28, 29, and 37. The numbers repeated 6 times are: 30, 32, 33, 34, 35, and 37. The numbers repeated 7 times are: 36, 38, 39, 40, 41, and 43. This pattern of groups of 6 elements seems to repeat with twin primes appearing in the same repeated group numbers.